Download Thevenin`s and Norton`s Theorems

Thevenin’s and Norton’s Theorems Say…
 That if we are only interested in current, voltage and power delivered
by a linear portion of a circuit, we can replace that portion (potentially a
large complex network,) by an equivalent circuit containing only an
independent source and a single resistor. The response will be
unchanged in the rest of the original circuit.
 Thevenin’s Theorem says that the independent source is a voltage
source and we should place it in series with the resistor. The theorem
also tells us how to calculate the value of the voltage source, Vs, and
the value of the resistance, Rt, called the Thevenin Resistance.
 Norton’s Theorem says that the independent source is a current
source and we should place it in parallel with the resistance. The
theorem also tell us how to calculate the value of the current source, Is,
and the value of the resistance, Rt, called the Thevenin Resistance.
 Of course, by source transformations, we can always switch from the
“Thevenin” equivalent circuit to the “Norton” equivalent circuit.
Rt
Vs
Thevenin Equivalent Network
Is
Rt
Norton Equivalent Network
To find the Thevenin Equivalent Network
1. First you must identify the network to find the equivalent of.
You can rearrange any circuit in the form of two networks connected by
two resistance-less conductors, labeled terminals A and B. (Note: If
either network contains a dependant source, its control variable must be
in the same network.)
If one of the networks is linear it can be replaced by this Thevenin
equivalent network:
The only thing left to do is find the values of Rt and Vs.
2. To find Vs:
Define a voltage, voc, as the open circuit voltage which would appear across the terminals A and B (of the
original network) if there was an open circuit between A and B. This voltage is Vs.
3. To find Rt:
There are three different cases that will require different methods to find R t:
a. If there are only independent sources in the network, then “kill” them.
Rt = Req
b. If there are dependant sources and independent sources in the network, find both voc and isc.
Rt = voc / isc .
c. If there are only dependent sources apply a 1A current source at the terminals A and B. Calculate the
resulting voltage, v, across this current source.
Rt = v / 1A
(Alternatively you can apply a 1V voltage source and measure resulting current, i, through it. Rt = 1V / i)
To find the Norton Equivalent Network
1. First you must identify the network to find the equivalent of.
You can rearrange any circuit in the form of two networks connected by
two resistance-less conductors, labeled terminals A and B. (Note: If
either network contains a dependant source, its control variable must be
in the same network.)
If one of the networks is linear it can be replaced by this Norton
equivalent network:
The only thing left to do is find the values of Rt and Is.
2. To find Is:
Define a current, isc, as the short circuit current which would be the current that would flow from terminal A to B
(of the original network) if A and B were short circuited. This current is Is.
3. To find Rt:
There are three different cases that will require different methods to find R t:
a. If there are only independent sources in the network then “kill” them.
Rt = Req
b. If there are dependant sources and independent sources in the network, find both voc and isc.
Rt = voc / isc .
c. If there are only dependent sources apply a 1A current source at the terminals A and B. Calculate the
resulting voltage, v, across this current source.
Rt = v / 1A
(Alternatively you can apply a 1V voltage source and measure resulting current, i, through it. R t = 1V / i)